A note on Vassiliev invariants of quasipositive knots

Sebastian Baader

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A note on Vassiliev invariants of quasipositive knots

Sebastian Baader

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Abstract

It has been known that any Alexander polynomial of a knot can be realized by a quasipositive knot. As a consequence, the Alexander polynomial cannot detect quasipositivity. In this paper we prove a similar result about Vassiliev invariants: for any oriented knot K and any natural number n there exists a quasipositive knot Q whose Vassiliev invariants of order less than or equal to n coincide with those of K.

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Sebastian Baader. 2005-04-13. A note on Vassiliev invariants of quasipositive knots. https://arxiv.org/abs/math/0412453

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